Profit Maximisation, Full cost, Pricing And Sales Maximisation

Introduction

The prime aim of
the neo-classical theory of the firm has been profit optimisation. But empirical proof
overwhelming point towards other objectives of firms, such as sales optimisation, output
optimisation, contentment optimisation and utility optimisation etc.

Profit Maximisation Theory

The firm maximises
its profits when it satisfies the two rules. MC = MR and the MC curve cuts the MR curve
from below. Maximum profits refer to pure profits which are excess above the average
cost of production. It is the amount left with the entrepreneur after he has made payments
to all factors of production, including wages of management. In other words, it is
a residual income over and above his normal profits. The profit maximisation condition
of the firm can be expressed as:

Maximise p (Q)

Where p (Q) = R(Q) – C(Q)

While p (Q) is profit, R(Q) is revenue and C(Q) are costs and Q are the units of output
sold. The two marginal rules and the profit maximisation condition stated above are
applicable both to a perfectly competitive firm and to a monopoly firm.

Profit Maximisation theory is based on the following Postulations.

Postulations

The objective of the firm is to maximise its profits where profits are the difference
between the firm’s revenue and costs

The entrepreneur is the single owner of the firm

Tastes and habits of consumers are given and are invariable

The firm produces a single, perfectly divisible and standardised commodity

The firm has complete knowledge about the amount of output which can be sold at
each price

The firm’s own demand and costs are known with certainty

New firms can enter the industry only in the long run. Entry of firms in the short
run is not possible

The firm maximises its profits over some time horizon

Techniques of production are given

Profits are maximised both in short run and long run

Based on the above postulations, the profit maximising model of the firm can be shown
under perfect competition and monopoly.

Profit Maximisation under Perfect Competition

Under
Perfect Competition the firm is one among large number of producers. It cannot
influence the market price of the product. It is the price taker and quantity adjuster.
It can only decide about the output to be sold at the market price. Hence, under conditions,
of perfect competition, the MR curve of a firm coincides with its AR curve. The MR
curve is horizontal to the X axis because the price is set by the market and the firm
sells its output at that price. The firm is thus, in equilibrium, when MC = MR = AR
(Price). The equilibrium of the profit maximisation firm under perfect competition
and is represented in the diagram 1, where the MC curve cuts the MR curve first at
point A.

It satisfies the condition of MC = MR, but it is not a point of maximum
profits because after point A, the MC curve is below MR curve. It does not pay the
firm to produce the minimum output when it can earn larger profits by producing beyond
OM. It will however, stop further production the minimum output when it reaches the
OM1 level of output where the firm satisfies both conditions of equilibrium. If it
has any plans to produce more equilibrium point B. Thus the firm maximises its profits
at M1B price and at output level OM1.

Profit Maximisation under Monopoly

There
being one seller of the product under monopoly, the monopoly firm in the industry itself.
Therefore, the demand curve for its product is downward sloping to the right, given
the tastes and incomes of its customers. It is a price maker which can set the price
to its maximum advantage. But it does not mean that the firm can set both price and
output. It can do either of two things. If the firm selects its output level, its price
is determined by the market demand for its product. Or if it sets the price for its
product, its output is determined by what consumers will take at that price.

In any
situation, the ultimate aim of the monopoly firm is to maximise its profits. The conditions
for equilibrium of the monopoly firm are (1) MC = MR < AR (Price) and (2) the MC
curve cuts the MR curve from below. It is represented in the diagram 2, that the profit
maximising level of output is OQ higher than MR, and the level of profit will fall.
If cost and demand conditions remain the same, the firm has no incentive to change
its price and output. The firm is said to be in equilibrium.

An illustration will let us know the optimisation of profits, revenue, sales and output.

Illustration

An industry faces demand curve given by 2Q = 200 – 4P. Marginal and Average Costs
for the industry are invariable at $20 per unit. Ascertain the following:

What must be the level of productivity, should the industry manufacture to optimise
profits,

To Optimise Sales Revenue,

Ascertain the corresponding profits at each productivity level.

SolutionCondition
1

The demand function
is specified, that is 2Q = 200- 4P.

We have to first convert the demand function into inverse function. Thus we derive the
following.

4P
= 200 – 2Q

P = 200 – 2Q
4

P = 50 – Q
2

Now, after obtaining this value, we have to equate MR with MC, for which we need to
derive Total Revenue TR.

Total
Revenue = Price x Quantity, Hence,

P . Q = 50Q – Q^2
2

Now, to obtain the Marginal Revenue, we have to apply the formula, dP.QdQ

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